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《离散数学及其应用(英文第7版)》课后答案

2021-03-22 11:13:19 类别:离散数学

  • 更新:2021-03-22 11:13:19
  • 大小:4.81 MB
  • 出版:机械工业出版社
  • 作者:Kenneth.H.Rosen
  • 类别:离散数学
  • 格式:PDF

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离散数学及其应用》(Discrete Mathematics and Its Applications)是经典的离散数学教材,为全球500多所大学广为采用作为指定教材。本书全面而系统地介绍了离散数学的理论和方法,内容涉及数学推理、组合分析、离散结构和算法设计。全书取材广泛,除包括定义、定理的严密陈述外,还配备大量的实例和图表的说明,各种练习和题目,以及丰富的历史资料和网站资源。本书适用于数学、计算机科学、计算机工程等专业的学生。

目录

  • preface iv
  • about theauthor xiii
  • the companion website xiv
  • to the studentxvi
  • list of symbols xix
  • 1 the foundations:logic and proofs
  • 1.1 propositional logic
  • 1.2 applications of propositional logic
  • 1.3 propositional equivalences
  • 1.4 predicates andquantifiers
  • 1.5 nested quantifiers
  • 1.6 rules of inference
  • 1.7 introduction to proofs
  • 1.8 proofmethods and strategy
  • end-of-chaptermaterial-
  • 2 basic structures:sets,functions,sequences,sums,andmatrices
  • 2.1 sets
  • 2.2 set operations
  • 2.3 functions
  • .2.4 sequences and summations
  • 2.5 cardinality of sets
  • 2.6 matrices
  • end-of-chaptermaterial
  • 3 algorithms
  • 3.1 algorithms
  • 3.2 the growth of functions
  • 3.3 complexity of algofithms
  • end-of-chapter material
  • 4 number theory and cryptography
  • 4.1 divisibilitv andmodular arithmetic
  • 4.2 integer representations andalgorithms
  • 4.3 primesand greatest common divisors
  • 4.4 solving congruences
  • 4.5 applications of congruences
  • 4.6 cryptography
  • end-of-chapter material
  • 5 induction and recursion
  • 5.1 mathematical induction
  • 5.2 strong induction and well-ordering
  • 5.3 recursive definitions and structural induction
  • 5.4 recursive algorithms
  • 5.5 program correctness
  • end-of-chapter material
  • 6 counting
  • 6.1 tlle basics of counting
  • 6.2 the pigeonhole principle
  • 6.3 permutations and combinations
  • 6.4 binomial coefficients and identities
  • 6.5 generalized permutations and combinations
  • 6.6 generating permutations and combinations
  • end-of-chapter material
  • 7 discrete probability
  • 7.1 an introduction to discrete probability
  • 7.2 probability theory
  • 7.3 bayes’theorem
  • 7.4 expected value and variance
  • end-of-chapter material
  • 8 advanced counring technigues
  • 8.1 applications of recurrence relations
  • 8.2 solving linear recurrence relations
  • 8.3 divide-and-conquer algorithms and recurrencerelations
  • 8.4 generating functions
  • 8.5 inclusion-exclusion
  • 8.6 applications of inclusion-exclusion
  • end—of-chapter material
  • 9 relations
  • 9.1 relations and their properties
  • 9.2 n-ary relations and theirapplications
  • 9.3 representing relations
  • 9.4 closures of relations
  • 9.5 equivalence relations
  • 9.6 partial orderings
  • end-of-chapter material
  • 10 graphs
  • 10.1 graphs andgraphmodels
  • 10.2 graph terminology and special types of graphs
  • 10.3 representing graphs and graph isomorphism
  • 10.4 connectivity
  • 10.5 eulerandhamiltonpaths
  • 10.6 shortest.pathproblems
  • 10.7 planargraphs
  • 10.8 graphcoloring
  • end-of-chapter material
  • 11 trees
  • 11.1 introduction to trees
  • 11.2 applications of trees
  • 11.3 tree travcrsal
  • 11.4 spanning trees
  • 11.5 minimum spanning trees
  • end-of-chapter material
  • 12 boolean algebra
  • 12.1 boolean functions
  • 12.2 representing boolean functions
  • 12.3 logic gates
  • 12.4 minimization of circuits
  • end-of-chapter material
  • 13 modeling cornputation
  • 13.1 languagesand grammars
  • 13.2 finite-state machines with output
  • 13.3 finite-state machines with no output
  • 13.4 languagerecognition
  • 13.5 turing machines
  • end-of-chapter material 

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